Sen. Susan Collins, R-Maine, asked Rosenstein at a budget hearing Tuesday what he would do if Trump ordered him to fire Mueller, who is investigating Russian interference in the USA elections and possible Russian ties to Trump's campaign.
In appointing Mueller last month, Rosenstein said that the "public interest requires me to place this investigation under the authority of a person who exercises a degree of independence from the normal chain of command".
Comey would not say in his testimony last week whether he thought the president sought to obstruct justice, but added it would be up to special counsel Mueller "to sort that out".
Comey told the committee that Trump encouraged him to drop an investigation into former national security adviser Michael Flynn, a claim the president has denied.
"No, I have not", he said.
Grassley and Feinstein met late Tuesday to discuss the Russian Federation matter following testimony from Attorney General Jeff Sessions before the Senate Intelligence Committee, Politico news reported.
Trump has made it clear that he is frustrated by the investigation into Russian interference in the presidential election, which USA intelligence officials have said was done to tilt the outcome in Trump's favor.
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The multi-tooled Hayes was drafted as a pitcher after serving as the Commodores' closer last season and registering seven saves. The Roselle, Ill., product headlined the Bears rotation for four seasons and earned Second Team All-Ivy honors as a senior.
Christopher Ruddy, a conservative publisher and a longtime friend of Trump, said Monday that Trump was considering removing Mueller, a former Federal Bureau of Investigation director who has been praised for his credibility by Republican and Democratic lawmakers.
Robert Mueller, the special counsel recently appointed to oversee the investigation into Russia's interference in the 2016 election is reported to beinterviewing senior intelligence officials.
Asked what he would do if Trump ordered him to fire Mueller, Rosenstein said, "I'm not going to follow any order unless I believe they are lawful and appropriate orders". Sessions recused himself from investigations related to the Trump campaign in February, a move that also provoked Trump's ire.
The sources, billed as familiar with Mueller's thinking, say the special counsel now views the matter as more than a simple "he said-he said" situation.
During the 1990s, President Bill Clinton and supporters protested the investigation of independent counsel Kenneth Starr, which began as a probe of the Whitewater real estate deal and ended with Clinton's impeachment on charges of perjury and obstruction regarding his relationship with intern Monica Lewinsky.
Comey testified to the Senate Intelligence Committee last week that he leaked information from memos he wrote describing his private conversations with Trump.
The ranking member of the House Intelligence Committee, Democrat Adam Schiff, responded forcefully by saying Mueller would be brought back "immediately".